Question

Monday 12 hours
Tuesday 8 hours
Wednesday 8 hours
Thursday 8 hours
Friday
10 hours
Garrett works at the pizza shop. He gets paid $14.00 per hour if he works 8 hours or less in a day. If Garrett works more than 8 hours in a day, he receives an extra $2.00 for every hour he works over 8 hours. For example, if Garrett works 10 hours, he receives $14.00 per hour for the first 8 hours and $16.00 per hour for the last 2 hours. The piecewise function represents the amount of money Garrett will make each day if he works x hours for the day. The table provides the hours Garrett worked each day for the week. Use the table and piecewise function to determine how much he will make for the week.
f (x) =
/ 14x,
0<x ≤8
16х - 16, 8 < x ≤ 24
(1 point)
• He will make $644.
• He will make $46.
• He will make $736.
• He will make $656

Answer 1

To calculate how much Garrett will make for the week, we'll use the piecewise function provided to find his daily earnings based on the number of hours he worked each day.

The piecewise function is:

\[
f(x) =
\begin{cases}
14x & \text{if } 0 < x \leq 8 \\
16x - 16 & \text{if } 8 < x \leq 24
\end{cases}
\]

Now, let's calculate his earnings for each day he worked:

1. **Monday: 12 hours**
\[
f(12) = 16(12) - 16 = 192 - 16 = 176
\]

2. **Tuesday: 8 hours**
\[
f(8) = 14(8) = 112
\]

3. **Wednesday: 8 hours**
\[
f(8) = 14(8) = 112
\]

4. **Thursday: 8 hours**
\[
f(8) = 14(8) = 112
\]

5. **Friday: 10 hours**
\[
f(10) = 16(10) - 16 = 160 - 16 = 144
\]

Now, let's summarize the earnings for each day:
- Monday: $176
- Tuesday: $112
- Wednesday: $112
- Thursday: $112
- Friday: $144

Now, let's add these amounts together to find the total earnings for the week:
\[
176 + 112 + 112 + 112 + 144 = 656
\]

So, Garrett will make **$656** for the week.